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# What is greatest positive integer n such that 2^n is a factor of 12^10

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Intern
Joined: 27 Sep 2011
Posts: 13
What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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26 Oct 2011, 23:06
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Difficulty:

5% (low)

Question Stats:

82% (00:58) correct 18% (01:07) wrong based on 253 sessions

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What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

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Joined: 21 Aug 2010
Posts: 174
Location: United States
GMAT 1: 700 Q49 V35
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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26 Oct 2011, 23:32
1
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

The given number is 12^10
=(2*2*3)^10
=(2^20)*(3^10)

So the greatest possible value for n such that 2^n can be factor of given number is 20.

Posted from my mobile device
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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27 Oct 2011, 04:02
2
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

$$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$
The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12!
Try this one.
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Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 27 Sep 2011
Posts: 13
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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27 Oct 2011, 07:03
VeritasPrepKarishma wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

$$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$
The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12!
Try this one.

Thank you very much.......... I am very weak in this type of PS math
Could you please explain 12! math you have given ?
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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27 Oct 2011, 19:32
VeritasPrepKarishma wrote:
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

$$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$
The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12!
Try this one.

n = 10

I just counted the number of 2s till 12 since the 12! is multiplication of all numbers till 12

Do you have any faster method which can be used for bigger factorials?
_________________

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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27 Oct 2011, 19:39
2
Check out this post: http://www.veritasprep.com/blog/2011/06 ... actorials/

It discusses how to solve such questions quickly.
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Karishma
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Joined: 02 Sep 2009
Posts: 52232
Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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07 Mar 2016, 08:36
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Similar question to practice: what-is-the-largest-integer-n-such-that-2-n-is-a-factor-of-158297.html
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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14 Mar 2016, 04:57
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10  [#permalink]

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02 Feb 2018, 10:28
Hi All,

This question comes down to exponent rules and how to 'rewrite' a number raised to a power.

12 = (2)(2)(3)

12^2 = (2^2)(2^2)(3^2) = (2^4)(3^2)
12^3 = (2^3)(2^3)(3^3) = (2^6)(3^3)

Seeing this pattern, you should be able to rewrite 12^10...

12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)

So the largest 'power of 2' that is a factor of 12^10 is 20.

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10 &nbs [#permalink] 02 Feb 2018, 10:28
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